Ideal amenability of module extensions of Banach algebras
Gordji, Eshaghi M. ; Habibian, F. ; Hayati, B.
Archivum Mathematicum, Tome 043 (2007), p. 177-184 / Harvested from Czech Digital Mathematics Library
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Let $\cal A$ be a Banach algebra. $\cal A$ is called ideally amenable if for every closed ideal $I$ of $\cal A$, the first cohomology group of $\cal A$ with coefficients in $I^*$ is zero, i.e. $H^1({\cal A}, I^*)=\lbrace 0\rbrace $. Some examples show that ideal amenability is different from weak amenability and amenability. Also for $n\in {N}$, $\cal A$ is called $n$-ideally amenable if for every closed ideal $I$ of $\cal A$, $H^1({\cal A},I^{(n)})=\lbrace 0\rbrace $. In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.

Publié le : 2007-01-01
Classification:  46Hxx 
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     author = {Eshaghi M. Gordji and F. Habibian and B. Hayati},
     title = {Ideal amenability of module extensions of Banach algebras},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {177-184},
     zbl = {1164.46020},
     mrnumber = {2354806},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108063}
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Gordji, Eshaghi M.; Habibian, F.; Hayati, B. Ideal amenability of module extensions of Banach algebras. Archivum Mathematicum, Tome 043 (2007) pp. 177-184. http://gdmltest.u-ga.fr/item/108063/

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